Rotund Gateaux smooth norms which are not locally uniformly rotund

Published 3 Mar 2023 in math.FA | (2303.01833v2)

Abstract: We provide, in every infinite-dimensional separable Banach space, an average locally uniformly rotund (and hence rotund) Gateaux smooth renorming which is not locally uniformly rotund. This solves an open problem posed by A.J. Guirao, V. Montesinos, and V. Zizler.

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